Geo-locating moving wireless devices

ABSTRACT

A method in a wireless device (WD) for determining a best-fit geo-location of a target station is described. The best-fit geo-location is determined using a plurality of round-trip times (RTTs). The target station is movable. The method includes assigning values to current target station parameters. The current target station parameters include a current location for the target station and movement parameters. A plurality of square residuals is determined based at least in part on the current target station parameters. Each square residual of the plurality of square residuals corresponds to one RTT. A minimum of a sum of squared residuals (SSR) is determined based at least on the plurality of square residuals. best-fit parameters are determined based at least in part on the determined minimum of the SSR. In addition, the best-fit geo-location of the target station is determined based at least on the best-fit parameters.

CROSS-REFERENCE TO RELATED APPLICATION

This application is related to and claims priority to U.S. ProvisionalPatent Application Ser. No. 63/110,567, filed Nov. 6, 2020, entitledGEO-LOCATING MOVING WIRELESS DEVICES, the entirety of which isincorporated herein by reference.

TECHNICAL FIELD

The present disclosure relates to geo-location of wireless devices, andin particular to a method and system for the geo-location of wirelesslocal area network (WLAN) devices.

BACKGROUND

Initially, it is noted that IEEE Standard 802.11-2016 is used as thebase reference for disclosures used herein, the entire contents of whichare incorporated herein by reference. The IEEE 802.11-2016 Standard iscommonly referred to as “Wi-Fi” and is referred to as such herein.

The location of wireless devices can be determined by various methods.These methods may be classified as active, passive, and combined activeand passive. In an active location scheme, a device that is determiningthe location or range, the measuring device transmits certain packets,referred to as “ranging packets”, to the device being located, i.e., thetarget device. A common method is to measure the time of arrival (TOA)of the response packet from the target device and compare that to thetime of departure (TOD) of the ranging packet that was transmitted bythe measuring device so as to determine the round trip time, RTT.

In an active location scheme, the TOD may be measured for a rangingpacket that is transmitted from the measuring station addressed to thetarget station. The TOA of the response from the target station at themeasuring station is then also measured. If the turnaround time for thetarget station to receive the packet from the measuring station and tostart to transmit the response is known, or is known to be a constant,then the time difference at the measuring station between the TOA andthe TOD, minus the turnaround time at the target station will bedirectly proportional to twice the distance of the target station fromthe measuring station. For example, if the target station is a wirelessdevice based upon IEEE 802.11 technology, and if the ranging packettransmitted from the measuring station to the target station is a datapacket, the response from the target station will normally be anacknowledgement (ACK) packet. If the ranging packet transmitted from themeasuring station to the target station is a control packet, for examplea request-to-send (RTS) packet, then the response from the targetstation will normally be a clear-to-send (CTS) packet. In these twoexamples, the turnaround time at the target station is defined in theIEEE 802.11 standard as the short interframe spacing (SIFS), which is apreset value. Hence, the time delay, td, or time of flight (TOF) betweenthe measuring station and the target station, may be determined from thecalculation td=(TOA−TOD−SIFS)/2 and the distance between the measuringstation and the target station is then td*c, where c is the speed oflight. This method of estimating the distance to a target station bymeasuring the TOD and TOA and accounting for the turnaround time isknown.

FIG. 1 is a diagram of a typical location system 100 which includesthree measuring stations 110 a, 110 b, and 110 c (referred tocollectively herein as “measuring stations” or “measuring receivers”110). The target station 120 may be a wireless device, such as, forexample, an Access Point (AP) that is to be located by the threeairborne measuring stations 110. The distance of the target station 120from measuring station 110 a is D1, 130. The distance of the targetstation 120 from measuring station 110 b is D2, 140. The distance of thetarget station 120 from measuring station 110 c is D3, 150. The roundtrip time, RTT1, determined from the calculation RTT=(TOA−TOD−SIFS), ismeasured for transmissions from measuring station 110 a and this can beused to calculate the distance D1 130 using the formula D1=RTT1*c/2where c is the speed of light. Similarly, RTT2 and RTT3 measurementsresult in the determination of distances D2 140 and D3 150. The methodsfor calculating the location of target station 120 using the distancesD1 130, D2 140, and D3 150 are well known.

FIG. 2 is a diagram of a location system where a single airbornemeasuring station 110 is used. The airborne measuring station 110 isdepicted being flown in an orbit 200 (e.g., circular orbit), centered atlocation E 220. Initially consider that a target station 120 isstationary at location F 230. The distance of the target station 120from the measuring station 110, when the measuring station 110 is atposition A 201, is D4 210. The distance of the target station 120 fromthe measuring station 110, when the measuring station 110 is at positionB 202, is D5 211. The distance of the target station 120 from themeasuring station 110, when the measuring station 110 is at position C203, is D6 212. The three RTT measurements taken when the airbornemeasuring station 110 is at positions A 201, B 202, and C 203 will yieldthe distances D4 210, D5 211, and D6 212, thus enabling the location F230 to be calculated. Consider the case where the target station 120, isnot stationary but moving with a constant velocity. In this example,when airborne measuring station 110 is at position B 202, target station120 is at location G 235 and when airborne measuring station 110 is atposition C 203, the target station 120 is at location H 236. In thiscase, the three RTTs will now correspond to distances D4 210, D15 215,and D16 216. From the RTT measurements D4 210 and D15 215, the locationof the target station 120 may be calculated to be at location P 250,where the arcs 240 and 242 for D4 and D15 respectively intercept, butwhen the RTT measurement D16 216 is taken, there is no single pointwhere all three arcs, 240 242 and 244, for D4, D15 and D16 respectively,intercept. The approximate location might be calculated as close to Q252, but with a large uncertainty. Hence, if the target station 120 isnot stationary, then in order to determine an accurate location thegeo-calculations should account for the movement.

FIG. 3 is a timing diagram that describes a ranging transmission methodof the present disclosure that may be used to determine the distancebetween two wireless devices: an airborne measuring station 110 and atarget station 120. Time axis 365 is the time axis for the airbornemeasuring station 110, and time axis 367 is the time axis for the targetstation 120. At time Ta 311, airborne measuring station 110 starts thetransmission of ranging packet 340 which is addressed to target station120. After a time-delay of td, at time Tb 321, target station 120 startsto receive ranging packet 340. At time Tc 312, airborne measuringstation 110 completes the transmission of ranging packet 340, and attime Td 322, target station 120 completes the reception of rangingpacket 340. The time difference between Tc 312 and Td 322 is td 331,which is the propagation time for the packet to travel from airbornemeasuring station 110 to target station 120. Note that the timedifferences (Tc−Ta) and (Td−Tb) are both the duration tp 330 of thetransmitted ranging packet 340.

Target station 120 transmits the response packet 345 at time Te 323.Assuming that the response packet 345 is an ACK or an RTS packet inreply to the received ranging packet 340, time Te 323 ideally will be ata time t_(SIFS) 332 after time Td 322, where t_(SIFS) 332 is the SIFStime as defined in the IEEE 802.11 standard. At time Tf 314, airbornemeasuring station 110 starts to receive the response packet 345. At timeTg 324, target station 120 completes the transmission of the responsepacket 345, and at time Th 325, airborne measuring station 110 completesreceiving the response packet 345. Note that the time differences(Tb−Ta), (Td−Tc), (Tf−Te), and (Th−Tg) are all equal and have the valuetd 331 which is the propagation time for the packet and response totravel between the two stations.

At airborne measuring station 110, the time of a packet at the pointwhen the frame check has completed, may be recorded. Hence, the time forthe transmission of ranging packet 340 that is recorded, is Tc 312, andthe time that is recorded for the reception of the response packet 345is Th 325. In order to calculate the value of td, it is desirable toknow the duration tr 334 of the response packet 345. Calculating theduration tr 334 is straightforward as the duration of the responsepacket 345 is defined in the Standard. In practice therefore, airbornemeasuring station 110 can calculate the value of td from expression (3):td=(Th−Tc−tr−t _(SIFS))/2  (2)and hence the corresponding distance, D=td*c  (3)

Stated another way, airborne measuring station 110 begins transmissionof ranging packet 340 at a beginning transmission time Ta 311 and endstransmission of the ranging packet 340 at an ending transmission time Tc312. Target station 120 receives the first ranging packet 340 at time Td322 and starts to transmit the response packet at time Te 323. Theairborne measuring station 110 receives the complete response packet 345at an ending reception time Th 314, wherein td 331 is measured as thetime (Th 325−Tc 312−tr 334−t_(SIFS) 332)/2.

A reception window Trw 360 may be defined which may be related to therange of the target station 120. The reception window starts at time Ts310 after the end of the transmission Tc 312 of ranging packet 340 andends at time Tt 320 after the end of the transmission Tc 312 of rangingpacket 340. As an example, the reception window Trw may be set to startat time Ts 310, 10 μs after time Tc 312, and end at time Tt 320, 60 μsafter time Tc 312. In this example the duration of the reception windowTrw 360 is 50 μs. Airborne measuring station 110 may transmit rangingpackets 340 at time intervals of Tp 350.

Hence, with reference again to FIG. 2 , in the general sense, as theairborne measuring station 110 flies around the target station 120transmitting ranging packets either continuously spaced at Tp 350 or inbursts of N transmissions, each transmission within the burst beingspaced at Tp 350. Airborne measuring station 110 will be measuring(i.e., measures, may measure, etc.) the RTT corresponding to its ownlocation (e.g., latitude, longitude, altitude). Based upon a set ofmeasured RTTs and corresponding airborne measuring station 110locations, and with knowledge of the ground elevation of the targetstation 120, the airborne measuring station 110 can estimate thedistance to the target station 120 using equations (2) and (3).

RTT measurements, in the general sense, will exhibit variations due tonoise, in the case of weak signal strengths, and, in part, the timingaccuracy of the clock at the target station 120 and the timing accuracyof the clock at the airborne measuring station 110. In addition, itshould be known that many Wi-Fi devices do not use the correct SIFS asper the IEEE 802.11 standard. Therefore, in order to derive an estimatedposition for the target station 120, the determination of a best fit tothe RTT measurements is required. The fitting of models to data when theequations are non-linear is a well-developed discipline and theclassical method for fitting RTT measurements to a target position is byuse of minimization of the summation of the squared residuals (SSR), aknown technique.

It should be known that in the case of very weak signal levels, and whencorrelation methods may be in use for the detection of the responsepacket 345, it is possible to falsely detect a response packet. In thepresence of such spurious RTT measurements, the use of the SSR techniqueto determine a best fit can produce errors in the estimated position ofthe target station 120.

As discussed above with reference to FIG. 2 , if the target station 120is not stationary, in order to derive an estimated position for thetarget station 120 and to determine a best fit to the RTT measurements,a further set of variables related to movement are required.

SUMMARY

Some embodiments advantageously provide methods, systems, andapparatuses for geo-locating moving wireless devices.

In one aspect of the present disclosure, a method for determining abest-fit geo location of a target station is described. The method isimplemented in a wireless device (WD), e.g., a measuring system,measuring station. The best-fit geo-location of the target station isdetermined using a plurality of round-trip times (RTTs), where each RTTis a time elapsed between a transmission of a ranging packet by the WDand a reception of a response packet by the WD. The target station ismovable. The method includes assigning values to current target stationparameters. The current target station parameters include a currentlocation for the target station 120 and movement parameters. A pluralityof square residuals is determined based at least in part on the currenttarget station parameters. Each square residual of the plurality ofsquare residuals corresponds to one RTT. A minimum of a sum of squaredresiduals (SSR) is determined based at least on the plurality of squareresiduals. Best-fit parameters are determined based at least in part onthe determined minimum of the SSR. The best-fit geo-location of thetarget station is determined based at least on the best-fit parameters.

In some embodiments, determining the plurality of square residualsfurther includes determining a first group of residuals based onstationary parameters and a second group of residuals based on themovement parameters, and for each of the first group and the secondgroup of residuals: determining a model fit probability based at leastin part on one of the determined first group of residuals and thedetermined second group of residuals; determining the SSR; performingnon-linear fitting based at least on the calculated SSR; determining newparameters based at least on the non-linear fitting; and determining newresiduals based at least in part on the determined new parameters.

In some other embodiments, performing non-linear fitting and determiningnew parameters are further based on a Levenberg-Marquardt process.

In an embodiment, the method further includes performing an F-test todetermine whether the non-linear fitting corresponding to the movingparameters is a better fit than the non-linear fitting corresponding tothe stationary parameters. If the non-linear fitting corresponding tothe moving parameters is the better fit, the non-linear fittingcorresponding to the moving parameters is used to determine the best-fitgeo-location. If the non-linear fitting corresponding to the movingparameters is not the better fit and one of a first condition is met anda second condition is met, the non-linear fitting corresponding to thestationary parameters to is used to determine the best-fit geo-location.The first condition is met when a first difference between an SSR and asubsequent SSR is less than a predetermined minimum. The secondcondition is met when an absolute value of a second difference between atarget station parameter and a subsequent target station parameter isless than the predetermined minimum.

In another embodiment, the first group of residuals is defined by:

$\mspace{76mu}{{f\left( {x_{i},\alpha} \right)} = {{\alpha^{OFF} + {\left( \frac{2}{c} \right)*{{d\left( {x_{i},\alpha} \right)}.{Where}}\mspace{14mu}{d\left( {x_{i},\alpha} \right)}}} = \left\lbrack {\quad{{\left( {x_{i}^{LAT} - \alpha^{LAT}} \right)^{2} + \left( {\left( {x_{i}^{L\; 0N} - \alpha^{LON}} \right)*{\cos\left( x_{i}^{LAT} \right)}} \right)^{2} + \left. \quad\left( \frac{x_{i}^{ALT} - \alpha^{ALT}}{CONVERSION} \right)^{2} \right\rbrack^{\frac{1}{2}}};}} \right.}}$

the second group of residuals is defined by:

$\mspace{76mu}{{{f\left( {x_{i},\alpha} \right)} = {\alpha^{OFF} + {\left( \frac{2}{c} \right)*{d\left( {x_{i},\alpha} \right)}}}},{{{Where}\mspace{14mu} d\left( {x_{i},\alpha} \right)} = \left\lbrack {{\left( {x_{i}^{LAT} - \left( {\alpha^{LAT} + {\alpha^{VelNorth}*x_{i}^{TD}}} \right)} \right)^{2} + \left( {\left( {x_{i}^{LON} - \left( {\alpha^{Lon} + {\alpha^{VelEast}*x_{i}^{TD}}} \right)} \right)*{\cos\left( x_{i}^{LAT} \right)}} \right)^{2} + \left. \quad\left( \frac{x_{i}^{ALT} - \alpha^{ALT}}{CONVERSION} \right)^{2} \right\rbrack^{\frac{1}{2}}},} \right.}}$

x_(i) represents WD location parameters,

α represents location parameters of the target station,

x_(i) ^(TD) is a negative time span of the corresponding RTT and acurrent time,

a^(VelEast) is in degrees latitude per time and is converted to aspherical coordinate by multiplying by cos(x_(i) ^(LAT)) beforeconverting units, and

CONVERSION refers to conversion of altitude units to geographic distanceunits, speed of light being in units of geographic distance divided byunits of RTT.

In some embodiments, the target station is moving, and the movementparameters include a first velocity vector in a first direction and asecond velocity vector in a second direction.

In some other embodiments, the method further includes measuring theplurality of RTTs; appending WD location parameters to each RTT of theplurality of RTTs, where the WD location parameters are associated witha location of the WD at a time of the reception of the response packetand are determined based in part on Global Positioning System (GPS)information; storing appended WD location parameters as records in adatabase; and when a preset period of time has elapsed and a number ofstored records in a dataset exceeds a predetermined number, retrievingthe stored records from the database to determine the plurality ofsquare residuals.

In an embodiment, the method further includes determining a targetlocation ellipse for the target station based on the determined best-fitparameters and performing the determination of the best-fit geo locationof the target station further based on the determined target locationellipse.

In another embodiment, the method further includes determining at leastone of a Jacobian matrix, a Hessian sum, and a correlation matrix todetermine the target location ellipse.

According to another aspect, a wireless device (WD) for determining ageo-location of a target station is described. The geo-location isdetermined using round-trip times (RTTs) of a plurality of signalstransmitted by the WD to the target station, and response signalsreceived from the target station corresponding to the transmittedsignals. The WD includes processing circuitry configured to assignvalues to current target station parameters, where the current targetstation parameters include a current location for the target station andmovement parameters; determine a plurality of square residuals based atleast in part on the current target station parameters, where eachsquare residual of the plurality of square residuals corresponding toone RTT; determine a minimum of a sum of squared residuals (SSR) basedat least on the plurality of square residuals; determine best-fitparameters based at least in part on the determined minimum of the SSR;and determine the best-fit geo-location of the target station based atleast on the best-fit parameters.

In some embodiments, determining the plurality of square residualsfurther includes determining a first group of residuals based onstationary parameters and a second group of residuals based on themovement parameters, and for each of the first group and the secondgroup of residuals: determining a model fit probability based at leastin part on one of the determined first group of residuals and thedetermined second group of residuals; determining the SSR; performingnon-linear fitting based at least on the calculated SSR; determining newparameters based at least on the non-linear fitting; and determining newresiduals based at least in part on the determined new parameters.

In some other embodiments, performing non-linear fitting and determiningnew parameters are further based on a Levenberg-Marquardt process.

In an embodiment, the processing circuitry is further configured toperform an F-test to determine whether the non-linear fittingcorresponding to the moving parameters is a better fit than thenon-linear fitting corresponding to the stationary parameters. If thenon-linear fitting corresponding to the moving parameters is the betterfit, the non-linear fitting corresponding to the moving parameters isused to determine the best-fit geo-location. If the non-linear fittingcorresponding to the moving parameters is not the better fit and one ofa first condition is met and a second condition is met, the non-linearfitting corresponding to the stationary parameters to is used todetermine the best-fit geo-location. The first condition is met when afirst difference between an SSR and a subsequent SSR is less than apredetermined minimum. The second condition is met when an absolutevalue of a second difference between a target station parameter and asubsequent target station parameter is less than the predeterminedminimum.

In another embodiment, the first group of residuals is defined by:

$\mspace{76mu}{{f\left( {x_{i},\alpha} \right)} = {{\alpha^{OFF} + {\left( \frac{2}{c} \right)*{{d\left( {x_{i},\alpha} \right)}.{Where}}\mspace{14mu}{d\left( {x_{i},\alpha} \right)}}} = \left\lbrack {\quad{{\left( {x_{i}^{LAT} - \alpha^{LAT}} \right)^{2} + \left( {\left( {x_{i}^{L\; 0N} - \alpha^{LON}} \right)*{\cos\left( x_{i}^{LAT} \right)}} \right)^{2} + \left. \quad\left( \frac{x_{i}^{ALT} - \alpha^{ALT}}{CONVERSION} \right)^{2} \right\rbrack^{\frac{1}{2}}};}} \right.}}$and

the second group of residuals is defined by:

$\mspace{76mu}{{{f\left( {x_{i},\alpha} \right)} = {\alpha^{OFF} + {\left( \frac{2}{c} \right)*{d\left( {x_{i},\alpha} \right)}}}},{{{Where}\mspace{14mu} d\left( {x_{i},\alpha} \right)} = \left\lbrack {{\left( {x_{i}^{LAT} - \left( {\alpha^{LAT} + {\alpha^{VelNorth}*x_{i}^{TD}}} \right)} \right)^{2} + \left( {\left( {x_{i}^{LON} - \left( {\alpha^{Lon} + {\alpha^{VelEast}*x_{i}^{TD}}} \right)} \right)*{\cos\left( x_{i}^{LAT} \right)}} \right)^{2} + \left. \quad\left( \frac{x_{i}^{ALT} - \alpha^{ALT}}{CONVERSION} \right)^{2} \right\rbrack^{\frac{1}{2}}},} \right.}}$

x_(i) represents WD location parameters,

α represents location parameters of the target station,

x_(i) ^(TD) is a negative time span of the corresponding RTT and acurrent time,

a^(VelEast) is in degrees latitude per time and is converted to aspherical coordinate by multiplying by cos(x_(i) ^(LAT)) beforeconverting units, and

CONVERSION refers to conversion of altitude units to geographic distanceunits, speed of light being in units of geographic distance divided byunits of RTT.

In some embodiments, the target station is moving, and the movementparameters include a first velocity vector in a first direction and asecond velocity vector in a second direction.

In some other embodiments, the WD further includes a transmitterreceiver in communication with the processing circuitry, where thetransmitter receiver is configured to measure the plurality of RTTs. Theprocessing circuitry is further configured to append WD locationparameters to each RTT of the plurality of RTTs, where the WD locationparameters are associated with a location of the WD at a time of thereception of the response packet and are determined based in part onGlobal Positioning System (GPS) information; store appended WD locationparameters as records in a database; and when a preset period of timehas elapsed and a number of stored records in a dataset exceeds apredetermined number, retrieve the stored records from the database todetermine the plurality of square residuals.

In an embodiment, the processing circuitry is further configured todetermine a target location ellipse for the target station based on thedetermined best-fit parameters; and perform the determination of thebest-fit geo location of the target station further based on thedetermined target location ellipse.

In some embodiments, the processing circuitry is further configured todetermine at least one of a Jacobian matrix, a Hessian sum, and acorrelation matrix to determine the target location ellipse.

According to another aspect, a measuring station for determining abest-fit geo-location of a target station is described. The best-fitgeo-location is determined using a plurality of round-trip times (RTTs),where each RTT is a time elapsed between a transmission of a rangingpacket by the measuring station and a reception of a response packet bythe measuring station. The measuring station includes a wireless deviceincluding a transmitter receiver configured to measure the plurality ofRTTs; and processing circuitry in communication with the transmitterreceiver. The processing circuitry is configured to assign values tocurrent target station parameters, where the current target stationparameters including a current location for the target station andmovement parameters; determine a plurality of square residuals based atleast in part on the current target station parameters, where eachsquare residual of the plurality of square residuals corresponds to oneRTT. Determining the plurality of square residuals includes determininga first group of residuals based on stationary parameters and a secondgroup of residuals based on the movement parameters; for each of thefirst group and the second group of residuals: determining a model fitprobability based at least in part on one of the determined first groupof residuals and the determined second group of residuals; determiningthe SSR; performing non-linear fitting based at least on the calculatedSSR; determining new parameters based at least on the non-linearfitting; and determining new residuals based at least in part on thedetermined new parameters. The processing circuitry is furtherconfigured to determine a minimum of a sum of squared residuals (SSR)based at least on the plurality of square residuals; determine best-fitparameters based at least in part on the determined minimum of the SSR;and determine the best-fit geo-location of the target station based atleast on the best-fit parameters.

In some embodiments, the processing circuitry is further configured toperform an F-test to determine whether the non-linear fittingcorresponding to the moving parameters is a better fit than thenon-linear fitting corresponding to the stationary parameters; if thenon-linear fitting corresponding to the moving parameters is the betterfit, use the non-linear fitting corresponding to the moving parametersto determine the best-fit geo-location; and, if the non-linear fittingcorresponding to the moving parameters is not the better fit and one ofa first condition is met and a second condition is met, use thenon-linear fitting corresponding to the stationary parameters todetermine the best-fit geo-location. The first condition is met when afirst difference between an SSR and a subsequent SSR is less than apredetermined minimum. The second condition is met when an absolutevalue of a second difference between a target station parameter and asubsequent target station parameter is less than the predeterminedminimum.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present disclosure, and theattendant advantages and features thereof, will be more readilyunderstood by reference to the following detailed description whenconsidered in conjunction with the accompanying drawings wherein:

FIG. 1 is a diagram of a typical location system which includes threemeasuring stations;

FIG. 2 is a diagram of a location system where a single airbornemeasuring station 110 is used;

FIG. 3 is a timing diagram that describes a ranging method of thepresent disclosure that may be used to determine the distance betweentwo wireless devices;

FIG. 4 is a diagram of a location system where a single airbornemeasuring station is used and the target station is moving from onelocation to another in accordance with the principles described herein;

FIG. 5 is an illustration of a moving target station together withillustrative calculated positions with and without the extra movingparameters, α^(VelNorth) and α^(VelEast), in accordance with theprinciples described herein;

FIG. 6 is a graphical representation of the RTT derived propagationtimes plotted against the positions as depicted in FIG. 5 in accordancewith the principles described herein;

FIG. 7 is a block diagram of an example measuring system that is used inaccordance with the principles described herein;

FIG. 8 is a flowchart of a non-limiting example of a method fordetermining the best fit model for a set of RTTs corresponding to atarget station moving at a constant velocity, and displaying thecorresponding calculated confidence ellipse of the location of thetarget station according to some embodiments of the present disclosure;

FIG. 9 is a flow diagram of an example process for determining thegeo-location of a target station that moves at a constant velocityaccording to some embodiments of the present disclosure; and

FIG. 10 is a flow diagram of an example process for determining abest-fit geo location of a target station according to some embodimentsof the present disclosure.

DETAILED DESCRIPTION

A method and devices are disclosed that determine the geo-location of amoving target station.

As described above with reference to FIG. 2 , based upon a set ofmeasured RTTs and corresponding airborne measuring station 110locations, and with knowledge of the ground elevation of the targetstation 120, the airborne measuring station 110 may estimate theposition of the target station 120.

A more complete understanding of the present disclosure, and theattendant advantages and features thereof, will be more readilyunderstood by describing the classical method for fitting the RTTmeasurements to a stationary target position by use of minimization ofthe summation of the squared residuals (SSR). The method for fitting theRTT measurements to a stationary target position by use of minimizationof the summation of the squared residuals (SSR) is known to one skilledin the art.

Assume there are N measurements with index i, of the RTT derivedpropagation time, y_(i), from the airborne measuring station 110 to thetarget station 120 target. For an arbitrary target location, the RTT maybe modelled by a function f(x_(i), α) where vectors x_(i) are the areknown locations of the airborne measuring station 110, latitude, x_(i)^(LAT), and longitude, x_(i) ^(LON) and altitude, x_(i) ^(ALT), andwhere parameter vector α defines the location of the target station 120in terms of latitude, α^(LAT), and longitude, α^(LON), and altitude,α^(ALT), plus other parameters that may include a turnaround offset,α^(OFF) to be determined. For example, α^(OFF) may include the error inthe SIFS of the target station 120.

The target location and offset, α^(LAT), α^(LON), α^(ALT), and offsetα^(OFF), may be determined by first defining a square residual, SR_(i).SR_(i) is the square of the difference between the measurement of RTTderived propagation time, e.g., using equation (2), y_(i), and thecomputation of total travel time, ƒ(x_(i), α).SR _(i) =[y _(i)−ƒ(x _(i),α)]²  (4)Where [y_(i)−ƒ(x_(i),α)] is the residual, R_(i) defined as thedifference of the RTT derived propagation time, y_(i), from the computeddistance multiplied by the factor (2/c) and modified by offset toconvert that distance to a model round trip time.

$\begin{matrix}{\mspace{76mu}{{f\left( {x_{i},\alpha} \right)} = {{\alpha^{OFF} + {\left( \frac{2}{c} \right)*{{d\left( {x_{i},\alpha} \right)}.{Where}}\mspace{14mu}{d\left( {x_{i},\alpha} \right)}}} = \left\lbrack {{\left( {x_{i}^{LAT} - \alpha^{LAT}} \right)^{2} + \left( {\left( {x_{i}^{L\; 0N} - \alpha^{LON}} \right)*{\cos\left( x_{i}^{LAT} \right)}} \right)^{2} + \left. \quad\left( \frac{x_{i}^{ALT} - \alpha^{ALT}}{CONVERSION} \right)^{2} \right\rbrack^{\frac{1}{2}}};} \right.}}} & (5)\end{matrix}$It is noted that the term “CONVERSION” refers to conversion of thealtitude units to the geographic distance units where the speed of lightis in the units of geographic distance divided by the units of RTT. Forexample, if latitude and longitude are used for location andmicroseconds are used for RTT, then c=0.0027027 degrees/microsecond.Longitude distances are scaled by the cosine of the latitude to accountfor spherical coordinates. All distances are sufficiently small to useplanar approximation.

Now consider the case of a moving target station 120. FIG. 4 is adiagram of a location system where a single airborne measuring station110 is used and the target station 120 is moving from location F 230, toG 235 to H 236. The airborne measuring station 110 is at location A 201,at time T_(A) 401: at location B 202, at time T_(B) 402; and at locationC 203, at time T_(C) 403. At time T_(A) 401, the target station 120 isat location F 230. At time T_(B) 402, the target station 120 is atlocation G 235. At time Tc 403, the target station 120 is at location H236. Assuming that the target station 120 is moving at a fixed velocityof ν, then the distance d_(BA) 440 between locations F 230 and G 235 isd _(BA)=ν(T _(B) −T _(A))Similarly, the distance d_(CB) 445 between locations G 235 and H 236 isd _(CB)=ν(T _(C) −T _(B))The durations (T_(B)−T_(A)) and (T_(C)−T_(B)) may be expressed as timedifferences, TD, where TD is the time that has elapsed since the lastRTT measurement.

The velocity ν may be resolved into two vectors, velocity in thenorthern direction and velocity in the eastern direction, namely“VelNorth” and “VelEast” respectively.ν=√{square root over ((VelEast)²+(VelNorth)²)}With reference again to FIG. 4 , the distance d_(BA) 440 can be resolvedinto VelEast×(T_(B)−T_(A)) 410 and VelNorth×(T_(B)−T_(A)) 412.Similarly, distance d_(CB) 445 can be resolved intoVelEast×(T_(C)−T_(B)) 420 and VelNorth×(T_(c)−T_(b)) 422. The distanced_(BA) 440 can be expressed as:d _(BA)=√{square root over ((VelEast*TD _(BA))²+(VelNorth*TD _(BA))²)}Where TD _(BA)=(T _(B) −T _(A))Similarly, the distance d_(CB) 445 can be expressed as:d _(CB)=√{square root over ((VelEast*TD _(CB))²+(VelNorth*TD _(CB))²)}Where TD _(CB)=(T _(C) −T _(B))

As discussed above for the stationary case, for an arbitrary targetlocation, the RTT may be modelled by a function f(x_(i), α) wherevectors x_(i) are the are known locations of the airborne measuringstation 110, latitude, x_(i) ^(LAT), and longitude, x_(i) ^(LON) andaltitude, x_(i) ^(ALT). In the case of a moving target, a vector elementx_(i) ^(TD) may be added to x_(i) which represents the (negative) timespan that has elapsed between time of the corresponding RTT and time ofthe current location. For the parameter vector α that defines thelocation of the target station 120 in terms of latitude, α^(LAT), andlongitude, α^(LON), and altitude, α^(ALT), and offset α^(OFF) additionalterms may be required. As a target station moves, the standard RTT modelfor the static case becomes unusable as the model assumes that all RTTsto contribute to a single location. Velocity terms, α^(VelNorth) andα^(VelEast), may be introduced as new parameters to represent a targetin motion. With these additional parameters, the RTTs no longer fit asingle location, and the model can account for changes in location dueto velocity and time to adjust the previous distances.

The moving target current location, velocity, and offset, α^(LAT),α^(LON), α^(ALT), α^(VelNorth), α^(VelEast) and α^(OFF), may now bedetermined by the square residual SR_(i) equation (5), and thecomputation of total travel time ƒ(x_(i), α), equation (6), where[y_(i)−ƒ(x_(i), α)] is the residual, R_(i) defined as the difference ofthe RTT derived propagation, e.g., time using equation (2), y_(i), fromthe computed distance multiplied by the factor (2/c) and modified byoffset to convert that distance to a model round trip time.

$\begin{matrix}{{f\left( {x_{i}\ ,a} \right)} = {\alpha^{OFF} + {\left( \frac{2}{c} \right)*{{d\left( {x_{i},a} \right)}.}}}} & (6)\end{matrix}$

For a moving target, however, d(x_(i), α) is now defined as follows:

$\begin{matrix}{{d\left( {x_{i},\alpha} \right)} = \left\lbrack {\left( {x_{i}^{LAT} - \left( {a^{LAT} + {a^{VelNorth}*x_{i}^{TD}}} \right)} \right)^{2} + \left( {x_{i}^{L\; 0N} - {\left( {\alpha^{LON} + \left( {a^{VelEast}*x_{i}^{TD}} \right)} \right)*\left. \quad{\cos\left( x_{i}^{LAT} \right)} \right)^{2}} + \left( \frac{x_{i}^{ALT} - \alpha^{ALT}}{CONVERSION} \right)^{2}} \right\rbrack^{\frac{1}{2}}} \right.} & (7)\end{matrix}$

Where α is the target current location parameters

-   -   x_(i) ^(TD) is the negative time span of the corresponding RTT        and the current time, and    -   α^(VelEast) is in degrees latitude per time and is converted to        the spherical coordinate by multiplying by cos(x_(i) ^(LAT))        before converting the units to mph or m/s        If the errors are Gaussian, then the best value for the target        location parameters, α, may be obtained by minimizing the sum of        the square residuals (SSR=Σ_(i) S R_(i)) which is defined by        setting the gradient of the SSR to zero:        0=∇_(α)(Σ_(i) SR _(i))=−2Σ_(i) [y _(i)−ƒ(x _(i),α_(i))][∇ _(α)        ƒ(x _(i),α_(i))]  (8)        A Jacobian J _(iα) may be defined as J _(iα)=∇_(α)ƒ(x        _(i),α_(i))  (9)        The Jacobian J_(iα) may be utilized to define the direction to        the minimum, known as the Steepest Descent method, may be        utilized to define the direction and step size to the minimum,        known as the Gauss-Newton method, or may be utilized to define        the end stage direction and step size to the minimum, known as        the Levenberg-Marquardt method.

Once this minimum is found, then the confidence ellipse can be foundusing the Jacobian J_(iα) evaluated with the parameter values determinedby the fit. In the first step the Hessian H_(α′α) may approximately bedefined byH _(α′α)=Σ_(i) [J _(iα)′]^(T) J _(iα)  (10)followed by a correlation matrix ρ_(α′α) defined as the inverse of theHessian H_(α′α):ρ_(α′α) =H _(α′α) ⁻¹  (11)Then a confidence ellipse, comprising length, width and orientation θ,may then be defined for the resulting location, as per Table 1:

Table 1—Location Confidence Ellipse ParametersTan(2Θ)=2*ρ₀₁/(ρ00−ρ11)Length²=ρ₀₀ Cos(Θ)Cos(Θ)+ρ₁₁ Sin(Θ)Sin(Θ)+2ρ₀₁ Cos(Θ)Sin(Θ)Width²=ρ₁₁ Cos(Θ)Cos(Θ)+ρ₀₀ Sin(Θ)Sin(Θ)−2ρ₀₁ Cos(Θ)Sin(Θ)

As discussed above, a standard technique to determining the best fit tofunction, ƒ(x_(i), α), is by utilization of the method of minimizationof sum of square residuals, SSR, also known as the least squareresiduals. For non-linear functions, such as ƒ(x_(i), α), there arevarious iterative methods that may be utilized including those known asSteepest Descent, Gauss-Newton, and Levenberg-Marquardt. These methodsshould be known to one skilled in the art.

FIG. 5 is an illustration of a moving target station 120 together withillustrative example calculated positions with and without the extramoving parameters, α^(VelNorth) and α^(VelEast). The airborne measuringstation 110 is depicted being flown in an orbit 500 (e.g., a circularorbit) starting at position 1 501 and continuing around the orbit 500 inan anticlockwise direction. Although the orbit 500 is shown in ananticlockwise direction, the orbit 500 is not limited as such and may bein any direction. Initially, consider that when the airborne measuringstation 110 is at position 1 501, the target station 120 is located at J550, travelling towards position K 555 at a constant velocity. Thedistance from the airborne measuring station 110 and the target station120 is d1 521. In this illustration, the target station 120 moves in aneasterly direction from location J 550 to location K 555 in the sametime that airborne measuring station 110 completes a full orbit startingat position 1 501 and ending at position 17 517, where positions 1 501and 17 517 represent a full orbit. For illustrative purposes it isassumed that the RTT, and hence the distance d between the airbornemeasuring station 110 and the target station 120, is measured every 22.5degrees of the orbit 500 at positions 1 501 through 17 517. For each22.5 degree of orbit, the airborne measuring station 110 will move1/16^(th) of the distance between locations J 550 and K 555. In thisexample the velocity north, VelNorth, of the target station 120 is zero,and the time difference TD is the time for the airborne measuringstation 110 to travel 22.5 degrees of orbit. When airborne measuringstation 110 is a position 2 502, the distance between the airbornemeasuring station 110 and the target station 120 is d2 502. Similarly,as the airborne measuring station 110 is at position 3 503 to 17 517,the distances to the target station are d3 523 to d17 537 respectively.

FIG. 6 is a graphical representation 600 of the RTT derived propagationtimes taken based on the pattern in FIG. 5 , plotted against thepositions 1 501 to 17 517. The measured RTTs propagation times, 605 arerelated to the distances d1 521 to d17 537. As discussed above withreference to equation (7) the best curve fit 610, which includes the“moving parameters” α^(VelEast), α^(VelNorth) fits the RTT propagationtimes 605. The best curve fit 620, however, does not fit the RTTpropagation times 605 because the fit is derived assuming a stationarytarget, as discussed above with reference to equation (6), i.e., thecurve fit 620 does not include the moving parameters. Referring again toFIG. 5 , the final estimated location of the target station 120,calculated using all the RTTs propagation times 605 as shown in FIG. 6 ,is at location L 545. The location L is depicted as a large arearepresenting a large uncertainty, as the best fit 620 has largedifferences to the measured RTT derived points, for example asdemonstrated by the difference 625 between the curve fit 620 and the RTTpropagation times 605 at the orbit position 4 in FIG. 6 . Conversely,final estimated location of the target station 120, as determined by thecurve fit 610 that includes the moving parameters, is at location K 555,the true location.

FIGS. 5 and 6 represent an example situation (e.g., an idealizedsituation) for ease of understanding in order to demonstrate anembodiment of this disclosure. In cases where a target station 120 ismoving at a constant velocity, by the inclusion of the “movingparameters” α^(VelEast), α^(VelNorth) in the square residual SR_(i)equation (5) and the computation of total travel time ƒ(x_(i), α), asused in equations (6) and (7), the updated location of the targetstation 120 can be continuously estimated. In the general case where thetarget station 120 may be changing velocity, provided that thevariations are not extreme, one half of an orbit may be required todetermine the average velocity. The validity of the addition of themoving parameters, to the stationary model parameters, may be tested byuse of the F-test. In the case that the F-test fails then the stationarymodel may be used.

FIG. 7 is a block diagram of an example measuring system 700 that isused in accordance with the principles described herein. In oneembodiment, measuring system 700 may be all or part of the airbornemeasuring station 110. In one embodiment, measuring system 700 mayinclude an antenna assembly 780, a transmitter receiver 710, a computersystem 730, a global positioning system (GPS) module 740, a gyro module760 and/or a network switch 750, such as an Ethernet switch. Measuringsystem 700 may be referred to as a wireless device (WD).

The transmitter receiver 710 may transmit or receive radio frequency(RF) signals to and from the antenna assembly 780. The GPS module 740output may be connected to the transmitter receiver 710. The GPS module740 may provide GPS information (e.g., location information), includingthe latitude, longitude, and altitude of the airborne platform. Thetransmitter receiver 710 may append the GPS information to any RFtransmission and/or reception. The network switch 750 may be connectedto the transmitter receiver 710, and the computer system 730. Thetransmitter receiver 710 may include a radio having a processor 711. Theprocessor need not be part of the radio. The GPS information may beprovided to the processor 711 by the GPS module 740. RF receptions mayhave the GPS information added such that the position of the airborneplatform is known for each received signal. The transmitter receiver 710may include more than one radio. Therefore, any transmission may beautomatically received by another radio within the transmitter receiver710, and by this means, the airborne platform position is also known foreach transmission. The GPS information may be sent to the network switch750 and therefore made available to the computer system 730.

The computer system 730 may include an interface 731. Interface 731 maycontain a connection (e.g., an Ethernet connection) to the networkswitch 750 (e.g., Ethernet switch), the connection to a display 736, aconnection to a keyboard and mouse 737 as well as interfacing to theprocessing circuitry 735. In some embodiments, the processing circuitry735 may include a processor 732, a memory 733, and/or a database 734.The database 734 may store the ground mapping information of the area ofinterest, and the processor 732 and memory 733 may be used to carry outthe exemplary processes 930 and/or 940 and/or any otherprocess/method/step, described in the present disclosure, usinginformation on the position of the airborne platform determined/derivedfrom the GPS module 740, the gyro module 760, and/or information on thetarget station 120 which may be inputted using the keyboard and mouse737. The display 736 may be used to show the ground map together withthe estimated location and/or confidence ellipse of the target station120 which may be derived using the example process 940, described below.Note that the modules discussed herein may be implemented in hardware ora combination of hardware and software. For example, the modules may beimplemented by a processor executing software instructions or byapplication specific integrated circuitry, e.g., processing circuitry,configured to implement the functions attributable to the modules. Alsonote that the term “connected to” as used herein refers to “being incommunication with” is not intended to mean a physical connection nor adirect connection, i.e., may be any type of connection/communication. Itis contemplated that the signal path between one element and another maytraverse multiple physical devices.

Thus, in some embodiments, the processing circuitry 735 may include thememory 733 and a processor 732, the memory 733 containing instructionswhich, when executed by the processor 732, configure the processor 732to perform the one or more functions/processes/methods/steps describedherein. In addition to a traditional processor and memory, theprocessing circuitry 735 may comprise integrated circuitry forprocessing and/or control, e.g., one or more processors and/or processorcores and/or FPGAs (Field Programmable Gate Array) and/or ASICs(Application Specific Integrated Circuitry).

The processing circuitry 735 may include and/or be connected to and/orbe configured for accessing (e.g., writing to and/or reading from) thememory 733, which may include any kind of volatile and/or non-volatilememory, e.g., cache and/or buffer memory and/or RAM (Random AccessMemory) and/or ROM (Read-Only Memory) and/or optical memory and/or EPROM(Erasable Programmable Read-Only Memory). Such memory 733 may beconfigured to store code executable by control circuitry and/or otherdata, e.g., data pertaining to communication, e.g., configuration and/oraddress data of nodes, etc. The processing circuitry 735 may beconfigured to control any of the methods described herein and/or tocause such methods to be performed, e.g., by the processor 732.Corresponding instructions may be stored in the memory 733, which may bereadable and/or readably connected to the processing circuitry 735. Inother words, the processing circuitry 735 may include a controller,which may comprise a microprocessor and/or microcontroller and/or FPGA(Field-Programmable Gate Array) device and/or ASIC (Application SpecificIntegrated Circuit) device. It may be considered that the processingcircuitry 735 includes or may be connected or connectable to memory,which may be configured to be accessible for reading and/or writing bythe controller and/or processing circuitry 735.

FIG. 8 is a flowchart of a non-limiting example of a method 800 fordetermining the best fit model for a set of RTTs corresponding to atarget station 120 moving at a constant velocity and displaying thecorresponding calculated confidence ellipse of the location of thetarget station 120 according to an embodiment of the disclosure.

Method 800 may include four processes:

Process 1—receiving RTTs, appending the positional data of the airbornestation, and storing the datasets in a database (steps 801, 802, and803);

Process 2—at preset intervals, inputting the datasets from the databaseand selecting initial parameters (steps 810, 811, 812 and 813);

Process 3—performing the minimizing of the sum of the squared residualsto find the best fit parameters (steps 814, 815, 816, 817, and 818); and

Process 4—calculating and displaying the location confidence ellipse forthe target station (steps 820, 821, 822, 823, 824, and 825).

The method 800 may start at step 801 where an RTT, y₁, is received. TheRTT may be the result of an exchange of a ranging packet 340 transmittedby transmitter receiver 710 and the reception of a response packet 345,from a target station 120, received by transmitter receiver 710 asdiscussed above with reference to FIGS. 3 and 7 . The locationcoordinates, x₁, of the measuring system 700 are appended to the RTT(Step 802). The processor 711 in the transmitter receiver 710 may obtainthe location coordinates from the GPS module 740, via the network switch750, and then append them to the RTT data. The RTT and location data,(y₁, x₁), are stored in a database 734 (Step 803), and the processreturns to step 801 where another RTT is received. Database 734 mayreside in the processing circuitry 735 in the computer system 730. EachRTT and location co-ordinates pair, (y₁, x₁), from processor 711 may besent to the database 734 residing in processing circuitry 735.

A loop timer is active (step 810). The loop timer may begin at thereception of the first RTT or when a user starts the location processvia the keyboard/mouse 737 (e.g., keyboard and/or mouse module). Forexample, a loop time of a predetermined interval of time, e.g., 5seconds, may be used, and hence step 810 may then output a signal everypredetermined interval of time, e.g., 5 seconds, to step 811. A checkmay be made at step 811 if there is an ongoing process active. Such aprocess may comprise Process 3, as outlined above. The loop timerfunction and the active process check may be performed by the processingcircuitry 735 in the computer system 730. If there is no ongoing processthe dataset (y_(i), x_(i)) is taken from the database 734 (step 812).Hence, for example, every 5 seconds the stored dataset, (y_(i), x_(i))is inputted from the database 734. Step 812 may include a check that thenumber of sets in the dataset exceeds a predetermined number. A set ofinitial parameters α are selected (step 813). The initial parameters αrepresent a starting location for the target station 120 in terms oflatitude, α^(LAT), longitude, α^(LON) and altitude α^(ALT), plus themoving parameters α^(VelEast), α^(VelNorth), and x_(i) ^(TD)′, and adistance measurement offset, α^(OFF). Any set of values may be used foran initial location. Examples for the starting location may include thelocation of the measuring system 700, as provided by the GPS module 740,or the location E 220 at the center of the orbit 200.

The two sets of residuals [y_(i)−ƒ(x_(i),α)], where ƒ(x_(i), α) isdefined by equation (5) for the stationary model and equation (6) forthe moving model, may be determined at step 814. Steps 814, 815, 816 and817 may comprise a loop where minimizing the sum of the square residualsis performed as described above with reference to equations (8), and(9). The loop modifies the parameters to find the best fit and continuesuntil the minimum conditions are met in step 816. The loop process isnow described. The sum of squared residuals, SSR, as discussed abovewith reference to equation (8), may be calculated (step 815). It may bedetermined, at step 816, if the minimum conditions have been met, and ifnot, the Levenberg-Marquardt non-linear fitting scheme may be performed,at step 817, to determine a next set of values for the α parameters.After completion of the calculations in step 817, the minimizationprocess returns to step 814. At step 816, two minimum conditions may bechecked to determine if the process has found the minimum (where jrefers to the current iteration and j−1 refers to the previousiteration):(SSR _(j) −SSR _(j−1))<Δ  Condition a)ABS|α _(j)−α_(j−1)|<Δ,  Condition b)where Δ has a very small value. For example, a value for Δ may be in theorder of 10⁻⁶. If either of these two conditions (i.e., a and/or b) ismet, in step 816, it is determined that the minimization loop process,steps 814, 815, 816, and 817, is complete, and step 816 may indicate tostep 811 that the process is complete. At completion of step 816 the twosets of parameters for the moving model and the stationary model areavailable. The minimization loop consisting of steps 814 to 817 may beperformed by the processing circuitry 735 in the computer system 730.

An F-test may be performed at step 818. An F-test may be used toindicate if the regression model using the moving parameters is a betterfit in terms of F-test than the model using the stationary parameters.If the F-test passes, then the process advances to step 820. If theF-test fails and the stationary model meets the minimum conditions atstep 816, then the process advances to step 820 using only thestationary model parameters. If the F-test fails and the stationarymodel does not meet the minimum conditions in step 816 then the processmay return to step 810, the loop timer. The F-test may be performed bythe processing circuitry 735 in the computer system 730. The use of theF-test is known to those skilled in the art of non-linear least squarefitting.

The Jacobian J_(iα), as discussed above with reference to equation (9),is determined at step 820. The Hessian H_(α′α), as described above withreference to equation (10), may be determined, at step 821, based uponthe Jacobian determined in step 820. The correlation matrix ρ_(α′α), asdescribed above with reference to equation (11), may be determined atstep 822. The location confidence ellipse parameters, as described abovewith reference to Table 1, may be calculated at step 823 and thelocation confidence ellipse parameters are sent to a display at step824. Steps 820 to 824 may be performed by the processing circuitry 735in the computer system 730. The display that is showing the targetlocation may be updated at step 825 with the new parameters from step823. Display 736 in the computer system 730 may be utilized as thedisplay for the location of the target station 120.

FIG. 9 is a flow diagram of an example process 900 for determining,according to some embodiments of the present disclosure, thegeo-location of a target station, moving at a constant velocity, usingan approach that utilizes a method of minimization of the summation ofthe squared residuals SSR. Process 900 may include four processes 910,920, 930 and 940 that correspond to the Process 1, Process 2, Process 3,and Process 4 described above with reference to FIG. 8 .

Process 900 starts with Process 1, 910. Process 1, 910 includes andstarts at step 911 where RTTs, y_(i), are received. The RTTs are theresult of exchanges of ranging packets 340 transmitted by transmitterreceiver 710 and the reception of response packets 345, from a targetstation 120, received by transmitter receiver 710, as discussed abovewith reference to FIGS. 3 and 4 . Note that the RTTs include the time tof the RTT. Process 1, 910 includes step 912 where the GPS locationco-ordinates x_(i) of the measuring system 700 (which is also theairborne measuring station 110), are appended to the RTTs. The locationcoordinates, corresponding to each received RTT, are obtained from theGPS module 740 and appended to the RTTs by the processor 711 in theTransmitter Receiver 710. Process 1, 910 includes step 913 where the RTTand location data, (y_(i), x_(i)), is stored in a database. The database734 resides in the processing circuitry 735 in the computer system 730and each RTT and location co-ordinates pair, (y_(i), x_(i)), fromprocessor 711, is sent to the database 734 residing in processingcircuitry 735. Process 1, 910, continues to run until a user terminatesthe location operation via the keyboard/mouse 737 which provides acommand to the processing circuitry 735 and the transmitter receiver 710to cease the operation. Hence, over time, the dataset in the database(step 913) becomes larger.

Process 2, 920, includes and starts with step 921 where the dataset inthe database (step 913) is inputted. The inputting of the dataset fromthe database is performed at a preset regular interval, e.g., 5 seconds.Step 921 is followed by step 922 where an initial set of parameters, α,are selected. These initial parameters represent a current location forthe target station 120 or the center of the orbit in terms of latitude,α^(LAT), longitude, α^(LON), and the corresponding ground altitude,α^(ALT), plus the moving parameters α^(VelEast), α^(VelNorth), plus adistance measurement offset, α^(OFF). The GPS parameters of themeasuring system 700 (which may also be the airborne measuring station110 and/or refer to a wireless device) or the center of the orbit, areused for α^(LAT), longitude, α^(LON), and corresponding ground altitude,α^(ALT), and a preset initial offset α^(OFF) of 314 μs or 60 μs is used(depending on spread spectrum technique), based upon a receive packetlength of 304 μs or 50 μs plus a SIFS of 10 μs. The GPS parameters areprovided by the GPS module 740. Initial values of zero are used for theparameters α^(VelEast), α^(VelNorth). Process 2, 920, is performed bythe processing circuitry 735 within the computer system 730. The datasetand the initial parameters are then inputted to Process 3, 930.

Process 3, 930, includes and starts with step 931 where a series ofdeterminations and calculations take place on the inputted data fromProcess 2, 920, step 922. In step 931, the two sets of residuals[y_(i)−ƒ(x_(i), α)] are first determined. One set of residuals isdefined by equation (5) for the stationary model and the other byequation (6) for the moving model. The sum of the squared residuals,SSR, for each model, is then calculated, as discussed above withreference to equations (4), (6) and (7). The determinations andcalculations in Step 931 are performed by the processing circuitry 935in the computer system 730. Process 3, 930, includes step 932 where twominimum conditions are checked to determine if the process has found theminimum. The conditions checked are:(SSR _(j) −SSR _(j−1))<10⁻⁶  Condition a)ABS|α _(j)−α_(j−1)|<10⁻⁶,  Condition b)where j refers to the current iteration and j−1 refers to the previousiteration. Process 3, 930 includes step 933. If neither condition (i.e.,a nor b) is met, then step 932 is followed by step 933 where theLevenberg-Marquardt non-linear fitting scheme is performed to determinenext values for the α_(j) parameters. These new parameters are thenpresented to step 931, and the minimization process, as described forsteps 931, 932 and 933 continues until, at step 932, one of theconditions (i.e., a or b) is true. If either condition, (i.e., a or b),is true then the parameters are inputted to Process 4, 940, and a signalis sent to Process 2, 920, step 921 informing at step 921 that theminimization has been completed for the last dataset that was inputtedfrom Process 2, 920, to Process 3, 930. If the preset regular interval,e.g., 5 seconds, has elapsed since Process 2, 920, inputted the lastdataset to Process 3, 930, then Process 2, 920, inputs the updatedcomplete dataset to Process 3, 930. If the preset regular interval,e.g., 5 seconds, has not elapsed since Process 2, 920, inputted the lastdataset to Process 3, 930, then Process 2, 920, waits until the presetregular interval, e.g., 5 seconds, has elapsed before inputting theupdated complete dataset to Process 3, 930.

Before exiting Process 3, an F-test is performed at step 934 to test ifthe model with the addition of the moving parameters α^(VelEast),α^(VelNorth) produces a better F-test fit than the nested model withjust the stationary parameters. If the F-test passes, then the processcontinues to Process 4 940. If the F-test fails and the stationary modelmeets the minimum conditions at step 932, then Process 4 proceeds usingthe stationary parameters. If the F-test fails and the stationary modeldoes not meet the minimum conditions, the process may return to 921 towait for a new input of datasets.

Process 4, 940, includes and starts with step 941 where Jacobian J_(iα),as discussed above with reference to equation (9), is determined. TheHessian H_(α′α), as described above with reference to equation (10), isthen determined based upon the Jacobian and the correlation matrixρ_(α′α), as described above with reference to equation (11), is alsodetermined followed by the calculation of the location confidenceellipse parameters, as described above with reference to Table 1.Process 4, 940, includes and step 941 is followed by step 942 where theupdated location ellipse parameters are sent to the display 736 in thecomputer system 730.

Process 900 continues until the user terminates the operation via thekeyboard/mouse 737.

The model fit as described above is valid as long as the velocity of thetarget station 120 is relatively constant. In order to derive a locationfor a moving target station 120, the airborne measuring station 110needs to complete a portion of its orbit that produces enough RTTstogether with a variation in subtended angles. In the general sense,about half an orbit for the airborne measuring station 110 is requiredsuch that a location for a moving target station 120 can be determined.The F-test as described above with reference to step 934 can be used tocheck if the moving parameters are still valid. This process is repeatedincluding new data at a regular time interval, for example, 5 seconds,so as to track the changing velocity.

FIG. 10 is a flow diagram of an example process 1000 for determining abest-fit geo location of a target station 120 according to someembodiments of the present disclosure. The process 1000 is implementedin a wireless device (WD), e.g., measuring system 700. One or moreblocks described herein, e.g., steps 1001-1005, may be performed by oneor more elements of the measuring system 700 such as by one or more ofprocessor 711, processor 732, processing circuitry 735, and transmitterreceiver 710. The best-fit geo-location of the target station 120 isdetermined using a plurality of round-trip times (RTTs), where each RTTis a time elapsed between a transmission of a ranging packet by the WD(e.g., measuring system 700) and a reception of a response packet by theWD. The target station 120 is movable. The process 1000 includes, atstep 1001, assigning values to current target station parameters. Thecurrent target station parameters include a current location for thetarget station 120 and movement parameters. At step 1002, a plurality ofsquare residuals is determined based at least in part on the currenttarget station parameters. Each square residual of the plurality ofsquare residuals corresponds to one RTT. At step 1003, a minimum of asum of squared residuals (SSR) is determined based at least on theplurality of square residuals. At step, 1004, best-fit parameters aredetermined based at least in part on the determined minimum of the SSR.Further, at step 1005, the best-fit geo-location of the target stationis determined based at least on the best-fit parameters.

In some embodiments, determining the plurality of square residualsfurther includes determining a first group of residuals based onstationary parameters and a second group of residuals based on themovement parameters, and for each of the first group and the secondgroup of residuals: determining a model fit probability based at leastin part on one of the determined first group of residuals and thedetermined second group of residuals; determining the SSR; performingnon-linear fitting based at least on the calculated SSR; determining newparameters based at least on the non-linear fitting; and determining newresiduals based at least in part on the determined new parameters.

In some other embodiments, performing non-linear fitting and determiningnew parameters are further based on a Levenberg-Marquardt process.

In an embodiment, process 1000 further includes performing an F-test todetermine whether the non-linear fitting corresponding to the movingparameters is a better fit than the non-linear fitting corresponding tothe stationary parameters. If the non-linear fitting corresponding tothe moving parameters is the better fit, the non-linear fittingcorresponding to the moving parameters is used to determine the best-fitgeo-location. If the non-linear fitting corresponding to the movingparameters is not the better fit and one of a first condition is met anda second condition is met, the non-linear fitting corresponding to thestationary parameters to is used to determine the best-fit geo-location.The first condition is met when a first difference between an SSR and asubsequent SSR is less than a predetermined minimum. The secondcondition is met when an absolute value of a second difference between atarget station parameter and a subsequent target station parameter isless than the predetermined minimum.

In another embodiment, the first group of residuals is defined by:

$\mspace{76mu}{{f\left( {x_{i},\alpha} \right)} = {{\alpha^{OFF} + {\left( \frac{2}{c} \right)*{{d\left( {x_{i},\alpha} \right)}.{Where}}\mspace{14mu}{d\left( {x_{i},\alpha} \right)}}} = \left\lbrack {{\left( {x_{i}^{LAT} - \alpha^{LAT}} \right)^{2} + \left( {\left( {x_{i}^{L\; 0N} - \alpha^{LON}} \right)*{\cos\left( x_{i}^{LAT} \right)}} \right)^{2} + \left. \quad\left( \frac{x_{i}^{ALT} - \alpha^{ALT}}{CONVERSION} \right)^{2} \right\rbrack^{\frac{1}{2}}};} \right.}}$and

the second group of residuals is defined by:

$\mspace{76mu}{{{f\left( {x_{i},\alpha} \right)} = {\alpha^{OFF} + {\left( \frac{2}{c} \right)*{d\left( {x_{i},\alpha} \right)}}}},{{{Where}\mspace{14mu} d\left( {x_{i},\alpha} \right)} = \left\lbrack {{\left( {x_{i}^{LAT} - \left( {\alpha^{LAT} + {\alpha^{VelNorth}*x_{i}^{TD}}} \right)} \right)^{2} + \left( {\left( {x_{i}^{LON} - \left( {\alpha^{LON} + {\alpha^{VelEast}*x_{i}^{TD}}} \right)} \right)*{\cos\left( x_{i}^{LAT} \right)}} \right)^{2} + \left. \quad\left( \frac{x_{i}^{ALT} - \alpha^{ALT}}{CONVERSION} \right)^{2} \right\rbrack^{\frac{1}{2}}},} \right.}}$

x_(i) represents WD location parameters,

α represents location parameters of the target station,

x_(i) ^(TD) is a negative time span of the corresponding RTT and acurrent time,

α^(VelEast) is in degrees latitude per time and is converted to aspherical coordinate by multiplying by cos(x_(i) ^(LAT)) beforeconverting units, and

CONVERSION refers to conversion of altitude units to geographic distanceunits where speed of light is in units of geographic distance divided byunits of RTT.

In some embodiments, the target station 120 is moving, and the movementparameters include a first velocity vector in a first direction and asecond velocity vector in a second direction.

In some other embodiments, the process 1000 further includes measuringthe plurality of RTTs; appending WD location parameters to each RTT ofthe plurality of RTTs, where the WD location parameters are associatedwith a location of the WD at a time of the reception of the responsepacket and are determined based in part on Global Positioning System(GPS) information; storing appended WD location parameters as records ina database; and when a preset period of time has elapsed and a number ofstored records in a dataset exceeds a predetermined number, retrievingthe stored records from the database to determine the plurality ofsquare residuals.

In an embodiment, the process 1000 further includes determining a targetlocation ellipse for the target station based on the determined best-fitparameters and performing the determination of the best-fit geo locationof the target station further based on the determined target locationellipse.

In another embodiment, the process 1000 further includes determining atleast one of a Jacobian matrix, a Hessian sum, and a correlation matrixto determine the target location ellipse.

Some embodiments of the present disclosure are as follows:

Embodiment 1. A method for a measuring station for determining a bestfit geo-location of a target station, the target station responding toranging packets transmitted by the measuring station, the methodcomprising:

measuring a plurality of round-trip times, RTTs, y_(i), each RTT being atime elapsed between a transmission of a ranging packet and a receptionof a response packet;

appending location parameters, x_(i), to each RTT, y_(i), the locationparameters being associated with the location of the measuring stationat a time of receipt of the response packet;

selecting initial parameters, α, the initial parameters representing:

-   -   a starting location for the target station; and    -   initial values for parameters related to movement;

iteratively calculating a minimum of a sum of squared residuals, SSR, tofind the best fit geo-location of the target station based at least onthe plurality of RTTs, y_(i), appended location parameters, x_(i), andinitial location and moving parameters α;

determining best fit parameters, α, for calculation of a target locationellipse for the target station;

calculating the target location ellipse for the target station; and

determining the best fit geo-location of the target station based atleast on the calculated target location ellipse.

Embodiment 2. The method of Embodiment 1, where the moving parameterscomprise a velocity in the North direction, “VelNorth”, and a velocityin the East direction, “VelEast”.

Embodiment 3 The method of Embodiment 1, further including after theappending of location parameters:

storing appended parameters (y_(i), x_(i)) as records in a database; and

when a preset period of time has elapsed and a number of the storedrecords in a dataset exceeds a predetermined number, retrieving thestored records from the database.

Embodiment 4. The method of Embodiment 1, wherein iterativelycalculating SSR further includes:

determining residuals for stationary and moving parameters, and for eachset of residuals:

calculating a model fit probability based at least on the determinedresiduals;

-   -   calculating a sum of squared residuals, SSR,    -   performing non-linear fitting based at least on the calculated        SSR;    -   determining new parameters α based at least on the non-linear        fitting; and    -   determining new residuals based at least in part on the        determined new parameters, α.

Embodiment 5. The method of Embodiment 4, wherein performing non-linearfitting and determining new parameters α are further based on aLevenberg-Marquardt method.

Embodiment 6 The method of Embodiment 4, further including performing anF-test to determine that the non-linear fitting using the best fitmoving parameters is a better fit in terms of F-test, than the modelusing the stationary parameters, and,

if true:

-   -   proceeding with the best fit moving parameters.

if false:

-   -   proceeding with the best fit stationary parameters

Embodiment 7. The method of Embodiment 1, wherein the locationparameters, x_(i), associated with the location of the measuring stationare provided by a GPS module.

Embodiment 8. The method of Embodiment 1, wherein the measuring stationis airborne.

Embodiment 9. The method of Embodiment 1, further including displayingthe calculated target locations ellipses and the best fit geo-locationsof the target station, as the target station is moving.

Embodiment 10. A wireless device for a measuring station for determininga best fit geo-location of a target station, the target stationresponding to ranging packets transmitted by the measuring station, thewireless device comprising:

a transmitter receiver configured to:

-   -   transmit a ranging packet;    -   receive a response packet in response to the transmitted ranging        packet; and    -   measure a plurality of RTTs, y_(i), each RTT being a time        elapsed between a transmission of a ranging packet and a        reception of a response packet; and

processing circuitry in communication with the transmitter receiver, theprocessing circuitry being configured to:

-   -   append location parameters, x_(i), to each RTT, y_(i), the        location parameters being associated with the location of the        measuring station at a time of receipt of the response packet;    -   select initial parameters, α, the initial parameters        representing:        -   a starting location for the target station; and        -   initial values for parameters related to movement;    -   iteratively calculate a minimum of a sum of squared residuals,        SSR, to find the best fit geo-location of the target station        based at least on the plurality of RTTs, y_(i), appended        location parameters, x_(i), and initial location and moving        parameters α;    -   determine best fit parameters, α, for calculation of a target        location ellipse for the target station;    -   calculate the target location ellipse for the target station;        and    -   determine the best fit geo-location of the target station based        at least on the calculated target location ellipse.

Embodiment 11. The wireless device of Embodiment 10, wherein the movingparameters comprise a velocity in the North direction, “VelNorth”, and avelocity in the East direction, “VelEast”.

Embodiment 12. The wireless device of Embodiment 10 wherein theprocessing circuitry, after the appending of location parameters, isfurther configured:

store appended parameters (y_(i), x_(i)) as records in a database; and

when a preset period of time has elapsed and a number of the storedrecords in a dataset exceeds a predetermined number, retrieve the storedrecords from the database.

Embodiment 13. The wireless device of Embodiment 10, wherein theprocessing circuitry, in order to calculate the SSR is furtherconfigured to:

determine residuals for stationary and moving parameters, and for eachset of residuals:

-   -   calculate a model fit probability based at least on the        determined residuals;    -   calculate a sum of squared residuals, SSR,    -   perform non-linear fitting based at least on the calculated SSR;    -   determine new parameters α based at least on the non-linear        fitting; and    -   determine new residuals based at least in part on the determined        new parameters, α.

Embodiment 14. The wireless device of Embodiment 13, wherein performingnon-linear fitting and determining new parameters α are further based ona Levenberg-Marquardt method.

Embodiment 15 The wireless device of Embodiment 13, wherein theprocessor is further configured to perform an F-test to determine thatthe non-linear fitting using the best fit moving parameters is a betterfit in terms of F-test, than the model using the stationary parameters,and,

if true:

-   -   proceed with the best fit moving parameters.

If false:

-   -   proceed with the best fit stationary parameters.

Embodiment 16. The wireless device of Embodiment 10, wherein thelocation parameters, x_(i), associated with the location of themeasuring station are provided by a GPS module.

Embodiment 17 The wireless device of Embodiment 10 wherein the measuringstation is airborne.

Embodiment 18. The wireless device of Embodiment 11, wherein themeasuring station is airborne.

Embodiment 19. A measuring station for determining a best fitgeo-location of a target station, the target station responding toranging packets transmitted by the measuring station, the measuringstation comprising:

a global positioning system (GPS) configured to:

-   -   provide location parameters associated with a location of the        measuring station; and

a wireless device in communication with the GPS, the wireless devicecomprising:

-   -   a transmitter receiver configured to:        -   transmit a ranging packet;        -   receive a response packet in response to the transmitted            ranging packet; and        -   measure a plurality of RTTs, y_(i), each RTT being a time            elapsed between a transmission of a ranging packet and a            reception of a response packet; and

processing circuitry in communication with the transmitter receiver, theprocessing circuitry being configured to:

-   -   append the location parameters, x_(i), to each RTT, y_(i), the        location parameters being associated with the location of the        measuring station at a time of receipt of the response packet;    -   store appended parameters (y_(i), x_(i)) as records in a        database;    -   when a preset period of time has elapsed and a number of the        stored records in a dataset exceeds a predetermined number,        retrieve the stored records from the database;    -   select initial parameters, α, the initial parameters        representing:        -   a starting location for the target station; and        -   initial values for parameters related to movement;    -   determine residuals for stationary and moving parameters, and        for each set of residuals:        -   calculate a model fit probability based at least on the            determined residuals;        -   calculate a sum of squared residuals, SSR,        -   perform non-linear fitting based at least on the calculated            SSR;        -   determine new parameters α based at least on the non-linear            fitting; and        -   determine new residuals based at least in part on the            determined new parameters, α;        -   iteratively calculate, using the Levenberg-Marquardt method            a minimum of a sum of squared residuals, SSR, to find the            best fit geo-location of the target station based at least            on the plurality of RTTs, y_(i), appended location            parameters, x_(i), and initial location and moving            parameters α;        -   perform an F-test to determine that the non-linear fitting            using the best fit moving parameters is a better fit in            terms of F-test, than the model using the stationary            parameters, and,        -   if true:            -   proceed with the best fit moving parameters.        -   if false:            -   proceed with the best fit stationary parameters;        -   determine new residuals based at least in part on the            determined new parameters; and        -   determine best fit parameters, α, for calculation of a            target location ellipse for the target station;    -   calculate the target location ellipse for the target station;        and    -   determine the best fit geo-location of the target station based        at least on the calculated target location ellipse.

The fitting of models to data when the equations are non-linear is awell-developed discipline used in diverse fields from physical sciences,to biology, to economics, to artificial intelligence and statistics ingeneral. As will be appreciated by one of skill in the art, the conceptsdescribed herein may be embodied as a method, data processing system,and/or computer program product. Accordingly, the concepts describedherein may take the form of an entirely hardware embodiment, an entirelysoftware embodiment or an embodiment combining software and hardwareaspects all generally referred to herein as a “circuit” or “module.”Furthermore, the disclosure may take the form of a computer programproduct on a tangible computer usable storage medium having computerprogram code embodied in the medium that can be executed by a computer.Any suitable tangible computer readable medium may be utilized includinghard disks, CD ROMs, optical storage devices, or magnetic storagedevices.

Some embodiments are described herein with reference to flowchartillustrations and/or block diagrams of methods, systems, and computerprogram products. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer program instructions. These computer program instructions maybe provided to a processor of a general purpose computer, specialpurpose computer, or other programmable data processing apparatus toproduce a machine, such that the instructions, which execute via theprocessor of the computer or other programmable data processingapparatus, create means for implementing the functions/acts specified inthe flowchart and/or block diagram block or blocks.

These computer program instructions may also be stored in a computerreadable memory that can direct a computer or other programmable dataprocessing apparatus to function in a particular manner, such that theinstructions stored in the computer readable memory produce an articleof manufacture including instruction means which implement thefunction/act specified in the flowchart and/or block diagram block orblocks.

The computer program instructions may also be loaded onto a computer orother programmable data processing apparatus to cause a series ofoperational steps to be performed on the computer or other programmableapparatus to produce a computer implemented process such that theinstructions which execute on the computer or other programmableapparatus provide steps for implementing the functions/acts specified inthe flowchart and/or block diagram block or blocks.

It is to be understood that the functions/acts noted in the blocks mayoccur out of the order noted in the operational illustrations. Forexample, two blocks shown in succession may in fact be executedsubstantially concurrently or the blocks may sometimes be executed inthe reverse order, depending upon the functionality/acts involved.Although some of the diagrams include arrows on communication paths toshow a primary direction of communication, it is to be understood thatcommunication may occur in the opposite direction to the depictedarrows.

Computer program code for carrying out operations of the conceptsdescribed herein may be written in an object-oriented programminglanguage such as Java® or C++. However, the computer program code forcarrying out operations of the disclosure may also be written inconventional procedural programming languages, such as the “C”programming language. The program code may execute entirely on theuser's computer, partly on the user's computer, as a stand-alonesoftware package, partly on the user's computer and partly on a remotecomputer or entirely on the remote computer. In the latter scenario, theremote computer may be connected to the user's computer through a localarea network (LAN) or a wide area network (WAN), or the connection maybe made to an external computer (for example, through the Internet usingan Internet Service Provider).

While the above description contains many specifics, these should not beconstrued as limitations on the scope, but rather as an exemplificationof several embodiments thereof. Many other variants are possibleincluding, for examples: the model parameters used, the variables used,the initial parameters used, the velocity vectors, the timing betweenRTTs, the section of orbit used to determine changes in velocity.Accordingly, the scope should be determined not by the embodimentsillustrated, but by their legal equivalents.

It will be appreciated by persons skilled in the art that the presentinvention is not limited to what has been particularly shown anddescribed herein above. In addition, unless mention was made above tothe contrary, it should be noted that all of the accompanying drawingsare not to scale. A variety of modifications and variations are possiblein light of the above teachings without departing from the scope of thefollowing claims.

What is claimed is:
 1. A method in a wireless device (WD) fordetermining a best-fit geo-location of a target station using aplurality of round-trip times (RTTs), each RTT being a time elapsedbetween a transmission of a ranging packet by the WD and a reception ofa response packet by the WD, the target station being movable, themethod comprising: assigning values to current target stationparameters, the current target station parameters including a currentlocation for the target station and movement parameters; determining aplurality of square residuals based at least in part on the currenttarget station parameters, each square residual of the plurality ofsquare residuals corresponding to one RTT, determining the plurality ofsquare residuals including: determining a first group of residuals basedon stationary parameters and a second group of residuals based on themovement parameters; for each of the first group and the second group ofresiduals: determining a model fit probability based at least in part onone of the determined first group of residuals and the determined secondgroup of residuals; determining a sum of squared residuals (SSR);performing non-linear fitting based at least on the determined SSR;determining new parameters based at least on the non-linear fitting;determining new residuals based at least in part on the determined newparameters; determining a minimum of the SSR based at least on theplurality of square residuals; determining best-fit parameters based atleast in part on the determined minimum of the SSR; performing an F-testto determine whether the non-linear fitting corresponding to movingparameters is a better fit than the non-linear fitting corresponding tothe stationary parameters; if the non-linear fitting corresponding tothe moving parameters is the better fit, using the non-linear fittingcorresponding to the moving parameters to determine the best-fitgeo-location; and if the non-linear fitting corresponding to the movingparameters is not the better fit and one of a first condition is met anda second condition is met, using the non-linear fitting corresponding tothe stationary parameters to determine the best-fit geo-location, thefirst condition being met when a first difference between the SSR and asubsequent SSR is less than a predetermined minimum, the secondcondition being met when an absolute value of a second differencebetween a target station parameter and a subsequent target stationparameter is less than the predetermined minimum; and determining thebest-fit geo-location of the target station based at least on thebest-fit parameters.
 2. The method of claim 1, wherein performingnon-linear fitting and determining new parameters are further based on aLevenberg-Marquardt process.
 3. The method of claim 1, wherein the firstgroup of residuals is defined by:$\mspace{76mu}{{f\left( {x_{i},\alpha} \right)} = {{\alpha^{OFF} + {\left( \frac{2}{c} \right)*{{d\left( {x_{i},\alpha} \right)}.{Where}}\mspace{14mu}{d\left( {x_{i},\alpha} \right)}}} = \left\lbrack {{\left( {x_{i}^{LAT} - \alpha^{LAT}} \right)^{2} + \left( {\left( {x_{i}^{L\; 0N} - \alpha^{LON}} \right)*{\cos\left( x_{i}^{LAT} \right)}} \right)^{2} + \left. \quad\left( \frac{x_{i}^{ALT} - \alpha^{ALT}}{CONVERSION} \right)^{2} \right\rbrack^{\frac{1}{2}}};} \right.}}$and the second group of residuals is defined by:$\mspace{76mu}{{{f\left( {x_{i},\alpha} \right)} = {\alpha^{OFF} + {\left( \frac{2}{c} \right)*{d\left( {x_{i},\alpha} \right)}}}},{{{Where}\mspace{14mu} d\left( {x_{i},\alpha} \right)} = \left\lbrack {{\left( {x_{i}^{LAT} - \left( {\alpha^{LAT} + {\alpha^{VelNorth}*x_{i}^{TD}}} \right)} \right)^{2} + \left( {\left( {x_{i}^{LON} - \left( {\alpha^{LON} + {\alpha^{VelEast}*x_{i}^{TD}}} \right)} \right)*{\cos\left( x_{i}^{LAT} \right)}} \right)^{2} + \left. \quad\left( \frac{x_{i}^{ALT} - \alpha^{ALT}}{CONVERSION} \right)^{2} \right\rbrack^{\frac{1}{2}}},} \right.}}$x_(i) represents WD location parameters, α represents locationparameters of the target station, x_(i) ^(TD) is a negative time span ofthe corresponding RTT and a current time, α^(VelEast) is in degreeslatitude per time and is converted to a spherical coordinate bymultiplying by cos(x_(i) ^(LAT)) before converting units, and CONVERSIONrefers to conversion of altitude units to geographic distance unitswhere speed of light is in units of geographic distance divided by unitsof RTT.
 4. The method of claim 1, wherein the target station is moving,and the movement parameters include a first velocity vector in a firstdirection and a second velocity vector in a second direction.
 5. Themethod of claim 1, the method further including: measuring the pluralityof RTTs; appending WD location parameters to each RTT of the pluralityof RTTs, the WD location parameters being associated with a location ofthe WD at a time of the reception of the response packet and beingdetermined based in part on Global Positioning System (GPS) information;storing appended WD location parameters as records in a database; andwhen a preset period of time has elapsed and a number of stored recordsin a dataset exceeds a predetermined number, retrieving the storedrecords from the database to determine the plurality of squareresiduals.
 6. The method of claim 1, the method further including:determining a target location ellipse for the target station based onthe determined best-fit parameters; and performing the determination ofthe best-fit geo location of the target station further based on thedetermined target location ellipse.
 7. The method of claim 6, the methodfurther including: determining at least one of a Jacobian matrix, aHessian sum, and a correlation matrix to determine the target locationellipse.
 8. A wireless device (WD) for determining a geo-location of atarget station using round-trip times (RTTs) of a plurality of signalstransmitted by the WD to the target station, and response signalsreceived from the target station corresponding to the transmittedsignals, the WD comprising processing circuitry configured to: assignvalues to current target station parameters, the current target stationparameters including a current location for the target station andmovement parameters; determine a plurality of square residuals based atleast in part on the current target station parameters, each squareresidual of the plurality of square residuals corresponding to one RTT,determining the plurality of square residuals including: determining afirst group of residuals based on stationary parameters and a secondgroup of residuals based on the movement parameters; for each of thefirst group and the second group of residuals: determining a model fitprobability based at least in part on one of the determined first groupof residuals and the determined second group of residuals; determining asum of squared residuals (SSR); performing non-linear fitting based atleast on the determined SSR; determining new parameters based at leaston the non-linear fitting; determining new residuals based at least inpart on the determined new parameters; determine a minimum of the SSRbased at least on the plurality of square residuals; determine best-fitparameters based at least in part on the determined minimum of the SSR;perform an F-test to determine whether the non-linear fittingcorresponding to moving parameters is a better fit than the non-linearfitting corresponding to the stationary parameters; if the non-linearfitting corresponding to the moving parameters is the better fit, usethe non-linear fitting corresponding to the moving parameters todetermine the best-fit geo-location; and if the non-linear fittingcorresponding to the moving parameters is not the better fit and one ofa first condition is met and a second condition is met, use thenon-linear fitting corresponding to the stationary parameters todetermine the best-fit geo-location, the first condition being met whena first difference between the SSR and a subsequent SSR is less than apredetermined minimum, the second condition being met when an absolutevalue of a second difference between a target station parameter and asubsequent target station parameter is less than the predeterminedminimum; and determine the best-fit geo-location of the target stationbased at least on the best-fit parameters.
 9. The WD of claim 8, whereinperforming non-linear fitting and determining new parameters are furtherbased on a Levenberg-Marquardt process.
 10. The WD of claim 8, whereinthe first group of residuals is defined by:$\mspace{76mu}{{f\left( {x_{i},\alpha} \right)} = {{\alpha^{OFF} + {\left( \frac{2}{c} \right)*{{d\left( {x_{i},\alpha} \right)}.{Where}}\mspace{14mu}{d\left( {x_{i},\alpha} \right)}}} = \left\lbrack {{\left( {x_{i}^{LAT} - \alpha^{LAT}} \right)^{2} + \left( {\left( {x_{i}^{L\; 0N} - \alpha^{LON}} \right)*{\cos\left( x_{i}^{LAT} \right)}} \right)^{2} + \left. \quad\left( \frac{x_{i}^{ALT} - \alpha^{ALT}}{CONVERSION} \right)^{2} \right\rbrack^{\frac{1}{2}}};} \right.}}$and the second group of residuals is defined by:$\mspace{76mu}{{{f\left( {x_{i},\alpha} \right)} = {\alpha^{OFF} + {\left( \frac{2}{c} \right)*{d\left( {x_{i},\alpha} \right)}}}},{{{Where}\mspace{14mu} d\left( {x_{i},\alpha} \right)} = \left\lbrack {{\left( {x_{i}^{LAT} - \left( {\alpha^{LAT} + {\alpha^{VelNorth}*x_{i}^{TD}}} \right)} \right)^{2} + \left( {\left( {x_{i}^{LON} - \left( {\alpha^{LON} + {\alpha^{VelEast}*x_{i}^{TD}}} \right)} \right)*{\cos\left( x_{i}^{LAT} \right)}} \right)^{2} + \left. \quad\left( \frac{x_{i}^{ALT} - \alpha^{ALT}}{CONVERSION} \right)^{2} \right\rbrack^{\frac{1}{2}}},} \right.}}$x_(i) represents WD location parameters, α represents locationparameters of the target station, x_(i) ^(TD) is a negative time span ofthe corresponding RTT and a current time, α^(VelEast) is in degreeslatitude per time and is converted to a spherical coordinate bymultiplying by cos(x_(i) ^(LAT)) before converting units, and CONVERSIONrefers to conversion of altitude units to geographic distance unitswhere speed of light is in units of geographic distance divided by unitsof RTT.
 11. The WD of claim 8, wherein the target station is moving, andthe movement parameters include a first velocity vector in a firstdirection and a second velocity vector in a second direction.
 12. The WDof claim 8, wherein the WD further comprises a transmitter receiver incommunication with the processing circuitry, the transmitter receiverbeing configured to: measure the plurality of RTTs; the processingcircuitry being further configured to: append WD location parameters toeach RTT of the plurality of RTTs, the WD location parameters beingassociated with a location of the WD at a time of the reception of theresponse packet and being determined based in part on Global PositioningSystem (GPS) information; store appended WD location parameters asrecords in a database; and when a preset period of time has elapsed anda number of stored records in a dataset exceeds a predetermined number,retrieve the stored records from the database to determine the pluralityof square residuals.
 13. The WD of claim 8, wherein the processingcircuitry is further configured to: determine a target location ellipsefor the target station based on the determined best-fit parameters; andperform the determination of the best-fit geo location of the targetstation further based on the determined target location ellipse.
 14. TheWD of claim 13, wherein the processing circuitry is further configuredto: determine at least one of a Jacobian matrix, a Hessian sum, and acorrelation matrix to determine the target location ellipse.
 15. Ameasuring station for determining a best-fit geo-location of a targetstation using a plurality of round-trip times (RTTs), each RTT being atime elapsed between a transmission of a ranging packet by the measuringstation and a reception of a response packet by the measuring station,the measuring station comprising: a wireless device comprising: atransmitter receiver configured to: measure the plurality of RTTs; andprocessing circuitry in communication with the transmitter receiver, theprocessing circuitry being configured to: assign values to currenttarget station parameters, the current target station parametersincluding a current location for the target station and movementparameters; determine a plurality of square residuals based at least inpart on the current target station parameters, each square residual ofthe plurality of square residuals corresponding to one RTT, determiningthe plurality of square residuals including: determining a first groupof residuals based on stationary parameters and a second group ofresiduals based on the movement parameters; for each of the first groupand the second group of residuals:  determining a model fit probabilitybased at least in part on one of the determined first group of residualsand the determined second group of residuals;  determining the SSR; performing non-linear fitting based at least on the determined SSR; determining new parameters based at least on the non-linear fitting;and  determining new residuals based at least in part on the determinednew parameters; determine a minimum of a sum of squared residuals (SSR)based at least on the plurality of square residuals; determine best-fitparameters based at least in part on the determined minimum of the SSR;perform an F-test to determine whether the non-linear fittingcorresponding to moving parameters is a better fit than the non-linearfitting corresponding to the stationary parameters; if the non-linearfitting corresponding to the moving parameters is the better fit, usethe non-linear fitting corresponding to the moving parameters todetermine the best-fit geo-location; and if the non-linear fittingcorresponding to the moving parameters is not the better fit and one ofa first condition is met and a second condition is met, use thenon-linear fitting corresponding to the stationary parameters todetermine the best-fit geo-location, the first condition being met whena first difference between an SSR and a subsequent SSR is less than apredetermined minimum, the second condition being met when an absolutevalue of a second difference between a target station parameter and asubsequent target station parameter is less than the predeterminedminimum; and determine the best-fit geo-location of the target stationbased at least on the best-fit parameters.